1. Field of the Invention
The present invention relates to improvements in the method of transiently manipulating dryer steam pressure in a paper machine during grade change.
Traditionally, steam pressure has been manipulated on the assumption that a change in the production amount of paper due to a change in dryer load varies linearly during grade change and such that the moisture percentage is changed by an appropriate amount to compensate the production amount change. For this reason, no compensation has been made for the non-linear part of the production amount change. Consequently, the moisture percentage momentarily rises above the target value in the course of grade change, causing problems in plant operation. Problems resulting from an increase in the moisture percentage include the following:
If the moisture percentage increases in the course of grade change, the paper in production may become crinkled or broken.
If the moisture percentage increases at the end of grade change, it will take a long time for the moisture percentage to return to the target value. Another problem is that the increase causes the moisture profile to deteriorate. Consequently, it will take a long time to completely change to the next type of product after grade change and therefore plant uptime is reduced.
To solve these problems, it is required to bring the moisture percentage as close as possible to the target value even during grade change. A general object of the present invention is to provide a method of manipulating steam pressure wherein a change in the production amount during grade change is precisely estimated and dryer steam pressure is manipulated so as to compensate the change in the production amount, so that the moisture percentage agrees with the target value during the grade change.
2. Description of the Prior Art
FIG. 1 is a diagrammatic view showing the configuration of a paper machine. Raw material discharged out of a headbox HB is dehydrated as the material passes through a wire part WP. Then, the material is dried out by a dryer DR and rolled round a reel RL. White water produced as the result of dehydration at the wire part WP is then received by a pit PT and fed back to the headbox HB by a fan pump PMP. Basis weight and moisture percentage are measured by a measuring instrument BM and input to a controller CMT. The controller CMT controls a stock control valve VLV according to the differences of the measured basis weight and moisture percentage from their target values, in order to adjust the inflow rate of raw material. The controller CMT also manipulates a steam pressure controller PRC to control steam pressure for drying. The component indicated by a symbol SB is a stock box where the raw material is contained.
When a grade change needs to be made, the controller CMT manipulates the stock control valve VLV to adjust the flow rate of raw material to be injected into the headbox HB and the machine speed. Furthermore, the controller CMT changes the manipulated variable of steam pressure to be output to the steam pressure controller PRC. In this case, a dead time occurs since there is a certain distance between the stock control valve VLV and the headbox HB. In addition, the system composed of the dryer DR has a large delay time constant. Control therefore must be carried out in consideration of the dead time and delay time constant when grade change is made. In the specifications of Japanese Patent Publication Nos. 11718 and 27437 of 1984, the applicant disclosed a method of steam pressure manipulation during grade change. The invention described in these publications will now be explained.
FIG. 2 is a diagrammatic view showing the configuration of a process model where the dead time and a first-order delay system are feed-forward controlled in an open loop. In this figure, the output of a feed-forward controller CON is applied to a process PRS through a hold circuit HLD. Consequently, a manipulation-caused moisture percentage change B(s) is obtained. Synthesizing the B(s) and a disturbance D(s) gives an actual moisture percentage change C(s).
Note here that the transfer functions H(s) and P(s) of the hold circuit HLD and process PRS are represented by the following formulas, respectively.                               H          ⁡                      (            s            )                          =                              1            -                          e                              -                Ts                                              s                                                  P          ⁡                      (            s            )                          =                              Ke                          -              Ls                                            1            +                                          T                0                            ⁢              s                                          
where
T=Sampling interval
To=Time constant
L=Dead time (L=m*T, where m is 0 or a natural number)
K=Process gain.
Z-transforming the composition of these two transfer functions gives the following result:                               HP          ⁡                      (            Z            )                          =                              Z            ⁡                          [                                                H                  ⁡                                      (                    s                    )                                                  *                                  P                  ⁡                                      (                    s                    )                                                              ]                                =                      Z            ⁡                          [                                                                    1                    -                                          e                                              -                        Ts                                                                              s                                *                                                      Ke                                          -                      Ls                                                                            1                    +                                                                  T                        0                                            ⁢                      s                                                                                  ]                                                              =                              K            ⁡                          (                              1                -                                  z                                      -                    1                                                              )                                ⁢                      z                          -              m                                *                      Z            ⁡                          [                              1                                  s                  ⁡                                      (                                          1                      +                                                                        T                          0                                                ⁢                        s                                                              )                                                              ]                                                              =                              K            ⁡                          (                              1                -                                  z                                      -                    1                                                              )                                ⁢                      z                          -              m                                *                      Z            ⁡                          [                                                1                  s                                -                                  1                                      s                    +                                          T                      0                                              -                        1                                                                                                        ]                                                              =                              K            ⁡                          (                              1                -                                  z                                      -                    1                                                              )                                ⁢                                    z                              -                m                                      ⁡                          (                                                1                                      1                    -                                          z                                              -                        1                                                                                            -                                  1                                      1                    -                                                                  e                                                                              -                            T                                                    /                                                      T                            0                                                                                              ⁢                                              z                                                  -                          1                                                                                                                                )                                                                        =                                                    K                ⁡                                  (                                      1                    -                    α                                    )                                            ⁢                              z                                  -                                      (                                          m                      +                      1                                        )                                                                                      1              -                              α                ⁢                                  xe2x80x83                                ⁢                                  z                                      -                    1                                                                                      ⁢                  
                ⁢                              where            ⁢                          xe2x80x83                        ⁢            α                    =                                    e                                                -                  T                                /                                  T                  0                                                      .                              
The necessary and sufficient conditions for G(z) in FIG. 2 to be able to settle finitely in the settling time of (N+m)xc2x7T (m is a natural number) are that equations 1.1 and 1.2 hold true for a given set of values a1, a2, . . . , aN, and A0, according to the final-value theorem, as shown below.                               G          ⁡                      (            z            )                          =                                            A              0                        ⁡                          (                              1                -                                  α                  ⁢                                      xe2x80x83                                    ⁢                                      z                                          -                      1                                                                                  )                                ⁢                      {                          1              +                                                a                  1                                ⁢                                  z                                      -                    1                                                              +                                                a                  2                                ⁢                                  z                                      -                    2                                                              +              …              +                                                a                                      N                    -                    1                                                  ⁢                                  z                                      -                                          (                                              N                        -                        1                                            )                                                                                                                              (        1.1        )                                                      lim                          z              ->              1                                ⁢                                    A              0                        ⁢                          K              ⁡                              (                                  1                  -                  α                                )                                      ⁢                          z                              -                                  (                                      m                    +                    1                                    )                                                      ⁢                          {                              1                +                                                      a                    1                                    ⁢                                      z                                          -                      1                                                                      +                                                      a                    2                                    ⁢                                      z                                          -                      2                                                                      +                …                +                                                      a                                          N                      -                      1                                                        ⁢                                      z                                          -                                              (                                                  N                          -                          1                                                )                                                                                                        }                                      =        1                            (        1.2        )            
From equation 1.2, we have       A    0    =      1                  K        ⁡                  (                      1            -            α                    )                    ⁢              (                  1          +                      a            1                    +                      a            2                    +          …          +                      a                          N              -              1                                      )            
By substituting this equation into equation 1.1, we obtain       G    ⁡          (      z      )        =                    1        -                  az                      -            1                                      KA        ⁡                  (                      1            -            α                    )                      ⁢          {              1        +                              ∑                          i              =              1                                      N              -              1                                ⁢                                    a              i                        ⁢                          z                              -                i                                                        }      
where A=1+al+a2+. . . +aNxe2x88x921.
By rearranging this equation for G(Z), we have                                                                         G                ⁡                                  (                  z                  )                                            =                              xe2x80x83                            ⁢                                                                    1                    -                                          α                      ⁢                                              xe2x80x83                                            ⁢                                              z                                                  -                          1                                                                                                                          KA                    ⁡                                          (                                              1                        -                        α                                            )                                                                      ⁢                                  {                                      1                    +                                                                  ∑                                                  i                          =                          1                                                                          N                          -                          1                                                                    ⁢                                              xe2x80x83                                            ⁢                                                                        a                          i                                                ⁢                                                  z                                                      -                            i                                                                                                                                }                                                                                                        =                              xe2x80x83                            ⁢                                                1                                      KA                    ⁡                                          (                                              1                        -                        α                                            )                                                                      ⁢                                  {                                      1                    +                                                                  (                                                                              a                            1                                                    -                          α                                                )                                            ⁢                                              z                                                  -                          1                                                                                      +                                                                  (                                                                              a                            2                                                    -                                                      α                            ⁢                                                          xe2x80x83                                                        ⁢                                                          a                              1                                                                                                      )                                            ⁢                                              z                                                  -                          2                                                                                      +                    …                    +                                                                                                                                          xe2x80x83                            ⁢                                                                                          (                                                                        a                                                      N                            -                            1                                                                          -                                                  α                          ⁢                                                      xe2x80x83                                                    ⁢                                                      a                                                          N                              -                              2                                                                                                                          )                                        ⁢                                          z                                              -                                                  (                                                      N                            -                            1                                                    )                                                                                                      -                                      α                    ⁢                                          xe2x80x83                                        ⁢                                          a                                              N                        -                        1                                                              ⁢                                          z                                              -                        N                                                                                            }                                                                        (        1.3        )            
At this point, the following holds true.                                                                                                               B                    ⁡                                          (                      z                      )                                                        =                                                                                    G                        ⁡                                                  (                          z                          )                                                                    ⁢                                              HP                        ⁡                                                  (                          z                          )                                                                                      =                                                                                            1                          -                                                      α                            ⁢                                                          xe2x80x83                                                        ⁢                                                          z                                                              -                                1                                                                                                                                                              KA                          ⁡                                                      (                                                          1                              -                              α                                                        )                                                                                              ⁢                                              {                                                  1                          +                                                                                    ∑                                                              i                                =                                1                                                                                            N                                -                                1                                                                                      ⁢                                                          xe2x80x83                                                        ⁢                                                                                          a                                i                                                            ⁢                                                              z                                                                  -                                  i                                                                                                                                                                    }                                            *                                                                                                    K                            ⁡                                                          (                                                              1                                -                                α                                                            )                                                                                ⁢                                                      z                                                          -                                                              (                                                                  m                                  +                                  1                                                                )                                                                                                                                                              1                          -                                                      α                            ⁢                                                          xe2x80x83                                                        ⁢                                                          z                                                              -                                1                                                                                                                                                                                                                                                                              =                                                                                    1                        A                                            ⁢                                              z                                                  -                                                      (                                                          m                              +                              1                                                        )                                                                                              ⁢                                              {                                                  1                          +                                                                                    ∑                                                              i                                =                                1                                                                                            N                                -                                1                                                                                      ⁢                                                          xe2x80x83                                                        ⁢                                                                                          a                                i                                                            ⁢                                                              z                                                                  -                                  i                                                                                                                                                                    }                                                              =                                                                  1                        A                                            ⁢                                              {                                                                              ∑                                                          i                              =                              0                                                                                      N                              -                              1                                                                                ⁢                                                      xe2x80x83                                                    ⁢                                                                                    a                              i                                                        ⁢                                                          z                                                              -                                                                  (                                                                      m                                    +                                    1                                    +                                    i                                                                    )                                                                                                                                                                    }                                                                                                                          ⁢                      
                    ⁢                                    where              ⁢                              xe2x80x83                            ⁢                              a                0                                      =            1.                          ⁢                  xe2x80x83                                    (        1.4        )            
Assuming a1=. . . =aNxe2x88x921=1 in equation 1.3, we have A=1+a1+. . . +aNxe2x88x921=N. Consequently,                                                                         G                ⁡                                  (                  z                  )                                            =                                                1                                      KA                    ⁡                                          (                                              1                        -                        α                                            )                                                                      ⁢                                  {                                      1                    +                                                                  (                                                  1                          -                          α                                                )                                            ⁢                                              z                                                  -                          1                                                                                      +                                                                  (                                                  1                          -                          α                                                )                                            ⁢                                              z                                                  -                          2                                                                                      +                    …                    +                                                                  (                                                  1                          -                          α                                                )                                            ⁢                                              z                                                  -                                                      (                                                          N                              -                              1                                                        )                                                                                                                -                                          α                      ⁢                                              xe2x80x83                                            ⁢                                              z                                                  -                          N                                                                                                      }                                                                                                        =                                                1                                      K                    *                    N                                                  ⁢                                  {                                                            1                                              1                        -                        α                                                              +                                          z                                              -                        1                                                              +                                          z                                              -                        2                                                              +                    …                    +                                          z                                              -                                                  (                                                      N                            -                            1                                                    )                                                                                      -                                                                  α                                                  1                          -                          α                                                                    ⁢                                              z                                                  -                          N                                                                                                      }                                                                                        (        1.5        )            
From the equation above, we obtain                               B          ⁡                      (            z            )                          =                              1            N                    ⁢                      {                                          ∑                                  i                  =                  0                                                  N                  -                  1                                            ⁢                              xe2x80x83                            ⁢                              z                                  -                                      (                                          m                      +                      i                      +                      1                                        )                                                                        }                                              (        1.6        )            
FIG. 3 illustrates the results of calculating equations 1.5 and 1.6 discussed above. The upper graph of FIG. 3 represents the transfer function G(z) of the controller CON, and the lower graph represents the moisture percentage change B(z). The horizontal axis indicates time. In the figure, the process gain K is defined as 1, and the values of N and m as 6 and 3, respectively. Thus, the method of steam pressure manipulation was prescribed according to equation 1.6, on the assumption that a change in the production amount during grade change was linear and such that the production amount change was cancelled by a change in the moisture percentage caused by steam pressure manipulation.
This means that according to FIG. 2, the actual moisture percentage C(s) is given by subtracting the manipulation-caused moisture percentage change B(s) from the disturbance D(s). Thus, control has been carried out on the assumption that the disturbance D(s) changes linearly and such that the B(s) is increased linearly from time t0 so as to compensate the disturbance D(s).
The present invention provides a method of manipulating dryer steam pressure in a paper machine during grade change. In the method, a change in the moisture percentage is determined from a change in the production amount during grade change, dryer steam pressure is manipulated so as to cancel the change in the moisture percentage, and the production amount in the course of grade change is calculated from basis weight and machine speed before and after the grade change.
The apparatus of the present invention for manipulating the dryer steam pressure comprises a first calculation part for calculating a steam pressure manipulation change value from a steam pressure prediction target value after grade change, a second calculation part for calculating another steam pressure manipulation change value from the nonlinear part of a change in the production amount, a multiplication part to which the output of the second calculation part is input so that the input value is multiplied by a weighting factor, and an addition part for summing the outputs of the multiplication part and first calculation part.
By using the dryer steam pressure manipulation apparatus and a steam pressure manipulation method described above, moisture percentage is kept constant during grade change so that such problems as sheet break are avoided and thereby plant uptime until the type of product is changed completely after grade change is increased.